I am trying to follow the developer's logic in telling you that insurance isn't needed. I reckon the developer is more concerned about the property insurance than board member protection. You may want to read the property's liability insurance to see if board member protection is included. It could be or it may not be.
I know as a former board member, that other board members refused to run for office if they weren't insured. Why would you want to risk YOUR PERSONAL assets on a bad decision be it in a group or as an individual? If you voted to remove all the streets signs in the community because they were "ugly", and someone has a vehicle accident because there was no "yield" sign, they could hold you personally liable without insurance. It was your neglect and decision that made you liable and the rest of the HOA.
Typically, there is a requirement to how much liability insurance your HOA must carry. It usually starts out at $1 million dollars. Mind you that isn't the payout amount one would win or acquire. If your board was to be sued for a bad decision such as the example, there is "cap". Our insurance "cap" was at about $60K. Most likely the court system would honor that amount if awarded. It's pretty much guaranteed money for the winner at that amount versus something higher. If the court does decide to award a higher award than the "cap" then ALL the homeowner's may be responsible for raising the difference. Say the winner won $100K and only $60K is covered by insurance. The leftover $40K would have to be picked up by the homeowner's.(HOA).
I highly recommend your HOA gets liability insurance. It can be expensive in some areas. Only a few companies do carry insurance for HOA's. Our policy even covered board member's if they were in car accidents during the carrying on of HOA business. If they got in an accident going to the MC's office, our insurance would "pick-up" the difference between what the owner's insurance paid out and the cost of total damages if there was a gap. We didn't own a HOA vehicle as described in our policy, but did use our private vehicles for HOA business. This is an option you may want to explore eliminating or keeping. It was part of our insurance no matter what.
Another insurance option that is "new" and available, is "Terrorist acts" coverage. If your area was to suffer an attack from a terrorist group, this insurance would cover some of it. It's just another option for you to consider when purchasing insurance. Make sure your not under insured or over insured. In our state, if your not in a designated "flood zone" you don't have to cover flooding. That can be expensive. Unfornately, we didn't fall into a "flood zone" but have 2-4 houses that continously flood during rain storms. We finally had to contact FEMA so the homeowner's insurance could be upgraded to cover flooding. The HOA's insurance didn't have to cover it but it did allow the individual's insurance to do so.
These are typical insurance issues beyond board member protection you may face. I'd suggest reviewing the options now before setting up a long term insurance contract. Many times insurance policies get ignored for years and the coverage is lacking by the time a claim is made 10 years from now. Our clubhouse is grossly under insured by atleast $20K. Allow for inflation or other increases in expenses when deciding how much to insure an amenity like a clubhouse. It's not going to often the insurance policy is going to be changed on the HOA's part but on the insurance companies whims.
Just get insurance and set it up well.

Recovering Ex-President of a HOA